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Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation

  • * Corresponding author: Liangjian Hu

    * Corresponding author: Liangjian Hu 

The author Wei Mao is supported by the National Natural Science Foundation of China (11401261) and "333 High-level Personnel Training Project" of Jiangsu Province. The author Liangjian Hu is supported by the National Natural Science Foundation of China (11471071). The author Xuerong Mao is supported by the Leverhulme Trust (RF-2015-385), the Royal Society (WM160014, Royal Society Wolfson Research Merit Award), the Royal Society and the Newton Fund (NA160317, Royal Society-Newton Advanced Fellowship), the EPSRC (EP/K503174/1)

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  • In this paper, we are concerned with the asymptotic properties and numerical analysis of the solution to hybrid stochastic differential equations with jumps. Applying the theory of M-matrices, we will study the $ p $th moment asymptotic boundedness and stability of the solution. Under the non-linear growth condition, we also show the convergence in probability of the Euler-Maruyama approximate solution to the true solution. Finally, some examples are provided to illustrate our new results.

    Mathematics Subject Classification: Primary: 60H10, 65C30.


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